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  1. C

    2D Harmonic Oscillator

    This might be another problem that our class hasn't covered material to answer yet - but I want to be sure. The question is the following: Find the eigenfunctions and eigenvalues of a two-dimensional isotropic harmonic oscillator. Again, I need help simply starting.
  2. C

    Infinite Potential Well

    Sorry for all the questions - I tend to save them till I'm done with assignments: Here's the question: Consider a particle of mass 'm' in a one-dimensional infinite potential well of width 'a' V (x) = \left\{\begin{array}{c} 0 \ \ \ if \ \ \ 0 \leq x \leq a \\ \infty \ \ \ otherwise...
  3. C

    Dirac delta function

    Can someone help me understand the transition between these two steps? <x> = \iint \Phi^* (p',t) \delta (p - p') \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t) \right) dp' dp = <x> = \int \Phi^* (p,t) \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t)...
  4. C

    Choosing a programming language - physics

    If I'm going to attempt creating computer programs for simulating theories as complicated as string theory, what language should I be looking at? I have some experience with C++, but if I'm going to devote a large part of my free time to learning a language, I'd like to learn something that...
  5. C

    Eigenfunctions and eigenvalues

    This is probably a straight forward question, but can someone show me how to solve this problem: \frac {d^2} {d \phi^2} f(\phi) = q f(\phi) I need to solve for f, and the solution indicates the answer is: f_{\substack{+\\-}} (\phi) = A e^{\substack{+\\-} \sqrt{q} \phi} I know...
  6. C

    Statics - Machines

    Here's the problem: "The bone rongeur shown [refer to attachment] is used in surgical procedures to cut small bones. Determine the magnitude of the forces exerted on the bone at E when two 25-lb forces are applied as shown." I understand that this "machine" can be broken into 4 free-body...
  7. C

    Inverse Laplace Transform

    I am asked to find the inverse laplace transform of the following function: \frac{ \left( s+3 \right) }{ \left( s+1 \right) \left( s+2 \right) } Using tables, can anyone help me understand why the answer is: 2e^{-t} - e^{-2t} I'm completely loss on this one, and yet the book...
  8. C

    Statics - 3D equilibrium problem

    Here's the question: "A camera of mass 240g is mounted on a small tripod of mass 200g. Assuming that the mass of the camera is uniformly distributed and that the line of action of the weight of the tripod passes through D, determine (a) the vertical components of the reactions at A, B, and C...
  9. C

    Calculating Spacing Using Ideal Gas Law

    Here's the question: For what temperatures are the atoms in an ideal gas at pressure P quantum mechanical? Hint: Use the idea gas law PV = N k_B T to deduce the interatomic spacing. Answer: T < \left( \frac{1}_{k_B} \right) \left( \frac{h^2}_{3m} \right)^{\left(...
  10. C

    Probability Density

    Here's the question: The needle on a broken car spedometer is free to swing, and bounces perfectly off the pins at either end, so that if you give it a flick it is equally likely to come to rest at any angle between 0 and \pi . Consider the x-coordinate of the needle point - that is, the...
  11. C

    Adding a constant V to the wave equation

    The question says to show that the wave function picks up a time-dependent phase factor, e^\left(-i V_0 t / \hbar \right) , when you add a constant V_0 to the potential energy. And then it asks what effect does this have on the expecation value of a dynamical variable? Assuming I only...
  12. C

    Time deritivate of the expectation value of p

    This is the problem: Calculate: \newcommand{\mean}[1]{{<\!\!{#1}\!\!>}} \frac {d \mean{p}}_{dt} Here's a few more points to keep in mind.... (A) The assumption is that <p> is defined as: \newcommand{\mean}[1]{{<\!\!{#1}\!\!>}} \mean{p} = -i \hbar \int \left( \psi^* \frac...
  13. C

    Expectation values of x and x^2

    Given the wave function: \psi (x,t) = Ae^ {-\lambda \mid x\mid}e^ {-(i ) \omega t} where A, \lambda , and \omega are positive real constants I'm asked to find the expectation values of x and x^2. I know that the values are given by <x> = \int_{-\infty}^{+\infty} x(A^2)e^...
  14. C

    Proving a force is conservative (via path integrals)

    It's always the easy questions that get me stuck.... For some reason, I'm having a mental block on how to answer this one: Consider the force function: F = ix + jy Verify that it is conservative by showing that the integral, \int F \cdot dr is independent of the path of integration...
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